Moon 3D This free app is a nice way to get the moon phase for any date. It has a graphic display of the moon's current phase, the dates of the next full and new moons, works in Southern or Northern hemisphere, and you can set any date in the past or future and see where the moon was/will be. The only downside is that it doesn't have the names of the phases, just pictures.

Moon Phase Pro This app costs .99 and will show you a moon calendar and what the moon phase was or will be for any date. It also shows you tons of other location-based moon data and has some very pretty animations to get the info across. Recommend!

Deluxe Moon - Moon Calendar This app costs 5.77 and has 5 different sizes/types of moon phase widgets, lets you swipe the moon to change the date, a moon calendar, a moon compass, and oodles of moon (and sun) info. The most comprehensive moon app on the Android Market.

Simple Moon Phase Widget This is exactly what it says that it is. Touching the widget will open a full moon calendar.

Moon phase widgets This is another great moon phase app that includes a nice feature for moon photographers: an exposure estimator for photographing the moon!